Abstract: Gielis transformations, with their origin in botany, are used to define square waves and trigonometric functions of higher order. They are rewritten in terms of Chebyshev polynomials. The origin of both, a uniform descriptor and the origin of orthogonal polynomials, can be traced back to a letter of Guido Grandi to Leibniz in 1713 on the mathematical description of the shape of flowers. In this way geometrical description and analytical tools are seamlessly combined.

Abstract: We generalize the Gielis Superformula by extending the R. Chacon approach, but avoiding the use of Jacobi elliptic functions. The obtained results are extended to the three-dimensional case. Several new shapes are derived by using the computer algebra system Mathematica(C).

Abstract: Addition of a labile sulphur donor to light sensitive silver halide microcrystals results in the formation of a distribution of silver sulphide clusters on the crystal surface. These silver sulphide clusters enhance the efficiency of image formation during the photographic process. Their activity towards the capturing of light photons, however, is very critical to their size (aggregation number) and concentration. By incorporating gold ions into silver sulphide clusters it was possible to monitor the size distribution by measuring the amount of gold reacted. From these experiments, no evidence was found for aggregation of the reacted sulphur entities on the surface. The uptake of gold ions at different sulphur concentrations could well be fitted with a simulated size distribution when a catalyzed deposition of sulphur was assumed, with a reactivity of the surface equal to 1.0 % for the microcrystals studied. From a simulation of the silver sulphide cluster size distribution a correlation could also be found between increasing aggregation numbers and the absorption at increasing wavelengths in diffuse reflectance spectroscopy.

Abstract: Optical (atomic absorption spectroscopy, AAS; atomic emission spectroscopy, AES; atomic fluorescence spectroscopy, AFS; and optogalvanic spectroscopy) and mass spectrometric (magnetic sector, quadrupolemass analyzer, QMA; quadrupole ion trap, QIT; Fourier transform ion cyclotron resonance, FTICR; and time-of-flight, TOF) instrumentation are well suited for coupling to the glow discharge (GD). The GD is a relatively simple device. A potential gradient (5001500 V) is applied between an anode and a cathode. In most cases, the sample is also the cathode. A noble gas (e.g. Ar, Ne, and Xe) is introduced into the discharge region before power initiation. When a potential is applied, electrons are accelerated toward the anode. As these electrons accelerate, they collide with gas atoms. A fraction of these collisions are of sufficient energy to remove an electron from a support gas atom, forming an ion. These ions are, in turn, accelerated toward the cathode. These ions impinge on the surface of the cathode, sputtering sample atoms from the surface. Sputtered atoms that do not redeposit on the surface diffuse into the excitation/ionization regions of the plasma where they can undergo excitation and/or ionization via a number of collisional processes. GD sources offer a number of distinct advantages that make them well suited for specific types of analyses. These sources afford direct analysis of solid samples, thus minimizing the sample preparation required for analysis. The nature of the plasma also provides mutually exclusive atomization and excitation processes that help to minimize the matrix effects that plague so many other elemental techniques. Unfortunately, the GD source functions optimally in a dry environment, making analysis of solutions more difficult. These sources also suffer from difficulties associated with analyzing nonconductingsamples. In this article, first, the principles of operation of the GD plasma are reviewed, with an emphasis on how those principles relate to optical spectroscopy and mass spectrometry. Basic applications of the GD techniques are considered next. These include bulk analysis, surface analysis, and the analysis of solution samples. The requirements necessary to obtain optical information are addressed following the analytical applications. This section focuses on the instrumentation needed to make optical measurements using the GD as an atomization/excitation source. Finally, mass spectrometric instrumentation and interfaces are addressed as they pertain to the use of a GD plasma as an ion source. GDsources provide analytically useful gas-phase species from solid samples. These sources can be interfaced with avariety of spectroscopic and spectrometric instruments for both quantitative and qualitative analysis.

Abstract: This paper proposes a new quantum mechanical model for the calculation of leakage currents. The model incorporates both variational calculus and the transfer matrix method to compute the subband energies and the life times of the inversion layer states. The use of variational calculus simplifies the subband energy calculation due to the analytical firm of the wave functions, which offers an attractive perspective towards the calculation of the electron mobility in the channel. The model can be extended to high-k dielectrics with several layers. Good agreement between experimental data and simulation results is obtained for metal gate capacitors.